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arXiv · 1809.09041

Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice

Jian Ding·Charles K Smart
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Abstract

We consider a Hamiltonian given by the Laplacian plus a Bernoulli potential on the two dimensional lattice. We prove that, for energies sufficiently close to the edge of the spectrum, the resolvent on a large square is likely to decay exponentially. This implies almost sure Anderson localization for energies sufficiently close to the edge of the spectrum. Our proof follows the program of Bourgain--Kenig, using a new unique continuation result inspired by a Liouville theorem of Buhovsky--Logunov--Malinnikova--Sodin.

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Jian Ding, Charles K Smart. 2018-09-24. Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice. https://arxiv.org/abs/1809.09041

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